Microfluidic-based systems are becoming widely used in biological and chemical analysis applications. Traditionally, flow cytometry focuses cells or particles, i.e., organize them into one or more stream lines. Typically, the stream lines are single file lines of cells or particles. For example, in conventional flow cytometry, a mixture or cells or particles in a carrier fluid is hydrodynamically focused using a sheath fluid to align cells or particles in one or more ordered streams. This active focusing requires that the practitioner manipulate the sample and control the flow conditions for the sheath fluid. It also requires vast reservoirs for sterile sheath fluid, complicating miniaturization of flow cytometers for point-of-care diagnostics.
After the cells or particles are focused into ordered streams, they can be counted. Alternatively, the cells or particles, which may be labeled with a fluorescent label or the like, could be interrogated using, for example, a laser or other optical apparatus to identify particular cells or particles of interest within the streams. After encapsulation in a droplet, the cells or particles of interest can then be deflected downstream of the interrogation region into an appropriate collection chamber or the like by using high-voltage electrical plates. For example, the cell or particle contained within the droplet of carrier fluid may be positively or negatively charged which can then be attracted (or repulsed) by the charged electrical plates. This causes movement of the droplets into the proper collection chamber for sorting after focusing.
Recently, various passive focusing systems and methods have been proposed for focusing cells or particles without a sheath fluid. See U.S. Patent App. Pub. No. 2009/0014360 to Toner et al. (“Toner et al.”), which is incorporated by reference herein. Toner et al. describes ordering of particles suspended in a fluid traveling through a microfluidic channel. The carrier fluid, the channel, and the pumping element are configured to cause inertial forces to act on and focus the cells and particles.
Fluid inertia is usually not considered important in microfluidic systems as the Reynolds number, the ratio of inertial to viscous forces is small, such that particles suspended in microfluidic flows have been expected to follow fluid streamlines (i.e., viscous forces dominate). Very recently, these inertial lift forces have also been shown to be extremely useful in microfluidic systems for a number of particle manipulation applications including focusing, ordering, separation, filtration, segregation, and extraction. For applications including focusing and separation, multiple geometries have been explored including straight channels, spirals, and asymmetrically curved turns. There is little and conflicting understanding of the underlying physical forces governing these systems and how to best design systems for separating arbitrary-sized particles at desired high rates. This understanding would enable practical high-throughput cell focusing, blood filtration, and water treatment in a cost-effective filterless platform.
Particle focusing in curved channels has been explained as a balance of lift forces from the wall, centrifugal forces, Saffman and Magnus forces, and Dean vortex flow. The Saffman and Magnus forces, in particular, require the assumption that particles lead or lag flow. Others contend particles are mostly entrained in flow, the result of a balance of inertial lift forces and entrainment in Dean flow. The relation between the Dean number and the Dean velocity has also been defined differently. Another area of incomplete understanding involves the inertial lift force. Some rely on derivations of the inertial lift force, which use a point-particle assumption, contrary to recent results suggesting a finite particle size assumption provides a more accurate description.
Inertial lift forces have been identified as one of the underlying players in focusing of particles of diameter, a, in channels of hydraulic diameter, Dh, at finite channel Reynolds numbers, RC=ρUDh/μ. Here ρ is the fluid density, μ is the fluid viscosity, and U is the mean channel velocity. Using point-particle assumptions the lift force leading to lateral migration and focusing was found to scale uniformly throughout the channel (FL=fLρU2a4/Dh2, where fL may be regarded as a lift coefficient dependent on the particle's position in the channel, the channel Reynolds number, and the aspect ratio of the channel). There appears to be a finite-particle size effect that leads to a more complex dependence of lift force on channel position and particle size: (FL=f1ρU2a3/Dh near the channel centerline and FL=f2ρU2a6/Dh4 near the wall). Assuming the near centerline scaling leads to slower lateral particle migration than near the channel wall, the lateral migration distance for a given downstream distance can be shown to be proportional to a particle Reynolds number, Rp(Rp=ρUa2/μDh).
In curved channel geometries non-intuitive lateral particle migration is observed. Secondary flows due to centrifugal effects on the fluid, i.e. Dean flow, have been postulated to act on particles and affect equilibrium positions but have not been systematically observed. Secondary flows capable of segregating suspended microparticles can also be generated by microstructured channels and leading to particle localization even at very high particle volume fractions. Dean flow is characterized by counter-rotating vortices such that flow at the midline of a channel cross-section is directed outward around a turn and, satisfying conservation of mass, slower moving fluid at the top and bottom of the channel is directed inward. Two dimensionless groups prescribe the flow in these channels of radius of curvature, r, the Dean number, De(De=RC(Dh/2r)1/2), and the curvature ratio, δ(δ=Dh/2r). Dean flow, scaling with De2 leads to a drag force upon particles lagging the secondary flow and directed in its direction. The maximum value of this force can be estimated by Stokes drag (FD˜ρU2aDh2r−1).
The current understanding of focusing in curved channel systems is based on previous work with asymmetrically curved channels and suggests a balance between inertial lift and entrainment by secondary vortices. There is a need for identification of important geometric factors of the microchannels that allow for further increases in throughput or focusing of potentially arbitrary particle sizes. There is also a need for inertial particle focusing systems configured for passive focusing at higher Reynolds numbers and throughputs. Further, there is a need for methods of designing microchannels for such systems that increase passive focus throughput for cells and particles of a known size.